A0561
Title: Regularizing BELIEF for smooth dependency
Authors: Wan Zhang - Chinese Academy of Sciences Center of Forecasting Science (China) [presenting]
Abstract: As the complexity of models and the volumes of data increase, interpretable methods for modeling complicated dependence are in great need. A recent framework of binary expansion linear effect (BELIEF) provides a "divide and conquer" approach to decompose any complex form of dependency into small linear regressions over data bits. Although BELIEF can be used to approximate any relationship, it faces an important challenge of high dimensionality. To overcome this obstacle, a novel definition of smoothness is proposed for binary interactions, and a regularization of BELIEF is created under smoothness interpretations. It has been proven that there is a one-on-one correspondence between each marginal binary interaction and the smoothness defined. Additionally, it is shown that in higher dimensions, the smoothness can be expressed as a product of marginal binary interactions. Based on these observations, it is proposed to model the smooth form of dependency with a generalized LASSO model with a larger penalty on less smooth terms. The numerical studies show that the smooth LASSO takes advantage of clear interpretability and effectiveness for nonlinear and high-dimensional data.
